WASHINGTON — President Obama and House Speaker John Boehner yesterday got down to the brass tacks in fiscal-cliff negotiations, with new details emerging that showed both sides ready to make major concessions.

Boehner (R-Ohio) proposed significant tax hikes, including raising rates on income over $1 million and, during yesterday’s talks, signaled he would back tax increases on investment income and dividends.

Obama counter-offered tax hikes on Americans earning over $400,000 — the first time he moved off his central demand that taxes go up for incomes over $250,000.

“Any movement away from the unrealistic offers the president has made previously is a step in the right direction, but a proposal that includes $1.3 trillion in revenue for only $930 billion in spending cuts cannot be considered balanced,” replied a Boehner spokesman.

The latest haggling, which included Obama and Boehner huddling at the White House for 45 minutes, indicated that the speaker had ended GOP opposition to Obama’s demand for higher tax rates on the rich.

Boehner first proposed the hike on millionaires in a phone call Friday. More details followed after yesterday’s meeting.

The Associated Press reported that under Boehner’s latest proposal, the top tax rate on capital gains would rise to 20 percent, up from the current 15 percent.

Obama may give in on reforms to cut spending on Social Security and other benefits.

Unless the White House and Congress can agree to an alternative debt-cutting plan, the fiscal cliff hits Jan. 1, with massive tax hikes for most Americans and deep federal spending cuts.

Economists predict that the double whammy of tax hikes and spending cuts would trigger another recession.

Boehner could pay a high political cost for making a bargain that raises tax rates. The deal could also fracture House Republicans.

The party’s conservative leaders and outside conservative activist groups have already taken aim at Boehner.